I need to delete a child’s iCloud account

One way to do this would be to log into the unwanted "child" account and request deletion of the Apple ID. You should have the ID and password from when you first set up the account.

From: How to delete your Apple ID account - How to delete your Apple ID account - Apple Support

Section: Can I delete my child’s account?

"Your child can also request deletion of their Apple ID, which requires your approval.

The approval request will be sent via email to the primary Apple ID email address of your family organizer account. When approving the request from this email, you will go through the process of deleting the child account."

If you have problems doing that then contact Apple about this request: Click here --> Choose your country or region - Official Apple Support Select your country, then a product and work your way down the menu to the desired issue. If you don't see one then try a different product until you reach a telephone or chat help request and ask to be redirected.